The acceleration of a particle, starting from rest, varies with time according to relation , `a =- r omega ^(2) sin ometa t`. Find the displacemnt of this particle at a time (t).

Explanation

Acceleration, ` a = (dv)/(dt) =- r omega sin omega t`.
or ` dv =- r omega ^(2) sin omega dt , `
Integratine it we have
` v=- r omega^(2) (-(cos omega t)/(ometa)) =r cos omega t`.
Now, velocity ` v= (dx)/(dt) =r omega cos omega t`
or ` dx= r ometa cos omega t dt`
Integrating it, we have
` x= r omega ((sin omega t)/(omega)) =r sin omega t`.